INK FAST: It’s not much of a head-scratcher, says Peter Vecsey, the Knicks should sign coach Mike Woodson to a contract extension before other jobs open up around the NBA.Anthony J. Causi

SCOTTSDALE, Ariz. — As long as the Knicks make the playoffs, and even if they don’t because of injuries, Mike Woodson will be the team’s biggest winner this season.

If this was an audition for an NBA head coaching job next season, he’s guaranteed to get the part. It will be up to Woodson to choose where to work. The opportunities will be plentiful, the offers fast and furious.

“Vacancy” signs will be flashing outside Portland, Washington and Charlotte, for sure, and figure to be lit up in Orlando, Los Angeles (should the Clippers crumble prematurely) and maybe even Phoenix, Milwaukee and Philadelphia.

Though it’s probably too early to reach any definitive decision, I fully expect James Dolan will lock up Woodson long-term long before the bidding can commence.

The reason Milwaukee is mentioned as possibly having an opening is, in part, because Scott Skiles has his home for sale. Said he’s looking to downscale.

Maybe so, but listing it while the season is in progress made everyone within the organization more nervous than they already were.

What kind of message does that send to the players, sponsors, season-ticket holders and owner Sen. Herb Kohl?

History tells us Skiles gets psychologically toasted near the end of his contract, as do his players. It happened in Phoenix and it happened in Chicago. He asked to leave in both instances, feeling he had lost the team. In each case, ownership gave permission and generously deducted a mere million dollars from the total amount.

A week or two prior to the March 15 trade deadline, the Bucks — players, staff and front office — sensed Skiles was getting frustrated, raising concern he was losing interest, again.

Nobody in the know can say Skiles was about to quit. Still, people were uneasy with what might be coming. After all, this is four years in Milwaukee going on five. There’s no doubt in anyone’s mind the acquisition of Monta Ellis has reinvigorated him — for how long is anybody’s guess.

The consensus of consenting adults identifies Skiles as one of the NBA’s top five coaches. He ascended to the top of the brain chain almost from the moment he checked into the league, which will mean zilch should he decide to check out on such a nasty number: $5 million.

I’ve hall-monitored the soon-to-be-retired senator since he purchased the Bucks in 1985 from the honorable Jim Fitzgerald. And one thing is for certain: Kohl will not pay a penny to a person who’s not on the job.

I listed Philly as a prospective employment site because Doug Collins is permanently in danger of suffering an emotional breakdown. His 29-23 76ers are down to seventh in the East, and are 9-14 since Feb. 15.

A cavalcade of couches (coaches too) are inching their way toward the City of Brotherly Love should they get totaled in the wee hours of the playoffs.

In spite of the Suns’ relative success — “We’ve overachieved thus far, frankly,” Steve Nash said Friday — the vibe in Phoenix is Alvin Gentry might not be rehired when his contract expires at season’s end.

In my preseason preview, I predicted Gentry would be the first coach cannibalized. Though he’s one of the lowest paid in the fraternity ($1 million, maybe less), I presumed he couldn’t survive with a cupboard so ridiculously bare. Especially when it was clear no major changes would be made until 2012-13, when owner Robert Sarver has a league-leading $31,582,020 of cap-space funds to spend on free agents.

Thibodeau is certain to repeat as Coach of the Year. Nevertheless, in view of the Suns’ playoff-contending 25-26 record, Gentry definitely deserves a high rung on the ballot — and a new deal.

This just in: Vultures went back into hiding after the Clips — on a late Chris Paul layup — edged the Blazers, minus LaMarcus Aldridge, Brandon Roy, Greg Oden and a real coach. Props to Jon Barry, who correctly opined before the game-winner that the Blazers had to get the ball out of Paul’s hands.

“If Walt Frazier wonders when was the last time he saw a player with Baron Davis’ skills in decline, he should study the film clips of himself as a Cavalier,” column contributor Phillip Marmanillo cracked.

This just in from column castigator Frank Drucker: John Calipari denied he ever had interest in Keith Olbermann’s latest former job.